The present invention is directed to a method and to a circuit arrangement for transmitting message cells via virtual paths of an asynchronous transfer mode (ATM) communication system. One such method and circuit arrangement has already been proposed by European Patent Application 93 110 320.4 (corresponding to U.S. Pat. No. 089,554, filed Jul. 12, 1993). The only thing set forth in this European patent application is that an alternate path is set up for each virtual path, this alternate path proceeding in the opposite direction and being used given outage of the regular virtual path. How such a switching can be implemented, however, is not discussed.